Understanding Logarithms
A logarithm is essentially the reverse operation of exponentiation. If you know that raising a base number to a certain power equals a specific result, the logarithm tells you what that specific power is. Our calculator allows you to compute logarithms for any custom base, including common logs and natural logs, and plots the mathematical curve for you instantly.
The Logarithmic Formula
The standard way to write and read a logarithm is:
This translates directly to the exponential equation:
- b (Base): The number being multiplied by itself.
- y (Exponent): The answer to the logarithm; how many times the base is multiplied.
- x (Argument): The resulting number.
What is a Natural Logarithm (ln)?
A natural logarithm has the base e (Euler's number, approximately 2.718). It is widely used in continuous compound interest, calculus, and physics to model natural growth and decay. In mathematics, it is written as ln(x) instead of loge(x).
Can a logarithm have a negative number?
No, logarithms of negative numbers are undefined in real numbers. This is because there is no real exponent you can apply to a positive base (like 10 or 2) that will result in a negative number.